"After what seemed like an eternity, the kid finally ran out of juice. Literally. " - means "after a long time the boy finished drinking juice (the juice finished)"
"Overcome by a paternal urge to pat him on the shoulder, but unable to find an adequate dry spot, I reached out with one finger and sort of ruffled his hair a bit." - father wanted to touch gently his son's shoulder (to show his love, maybe) but after thinking a little he decided only to ruffle his son's hair with one finger"